The present invention relates generally to eddy current examinations of a material and, more particularly, to a method, an apparatus, and an article of manufacture for modeling eddy current probes and simulating eddy current examinations of a material.
Modeling complex eddy current probes and simulating eddy current examinations of a material is critical to the design of eddy current inspection systems. The increasing demand for specialized eddy current probes has created a need for the modeling of more complex eddy current probes and the simulation of more complex eddy current examinations.
Eddy current examination simulations are a valuable tool in the design and optimization of eddy current probes. A simulated eddy current examination generates the response of the eddy current probe for a series of scans of a material. Further, the simulated eddy current examination provides insight into the physics of the interaction between the material, a flaw in the material, and the eddy current probe. With simulated eddy current examinations, improved eddy current probe design for increasingly specialized eddy current examinations can be accomplished.
Three different numerical techniques are commonly used to model eddy current probes and to simulate eddy current examinations: the finite element method ("FEM"), the volume integral method ("VIM"), and the boundary element method ("BEM").
Of the three numerical techniques, the FEM is the most general numerical technique with the capability of modeling an eddy current probe of any geometry and made with any material. Computer software packages for generating models of an eddy current probe using the FEM are commercially available, and one such package is the "EMAS" package developed by Ansoft Corp., Pittsburgh, Pa. For conventional use of the FEM, a volume mesh is generated which includes the eddy current probe, the material to be examined, which typically includes a flaw, and the surrounding fluid, which is typically air. The field solution is determined for every point in the space of the volume mesh.
The output impedance of the modeled eddy current probe is determined from the field solution and is a single value for the eddy current probe at a fixed location with respect to the material, and more particularly with respect to the flaw in the material. In order to obtain the output impedance of the modeled eddy current probe for a scan across the material, a new volume mesh and a new field solution must be determined for each point in the scan. Further, to obtain a simulated eddy current examination of the material, a series of scans across the material is required, and a new volume mesh and a new field solution must be determined for each point in each scan. This is a very time consuming procedure.
Because the volume mesh generation is so time intensive, it is impractical to generate a simulated eddy current examination of the material with the FEM for a scan across the material, and impractical for a series of scans across the material. Instead, the FEM is used for understanding the physics of the interaction between the eddy current probe, the material, and, if present, the flaw in the material.
In addition to the FEM, the VIM and the BEM are two numerical techniques which can be adapted to generate an eddy current examination of a material. See W. S. Dunbar, "The Volume Integral Method of Eddy Current Modeling," J. Nondestructive Eval., 5:9-14 (1985); D. M. McKirdy, "Recent Improvements to the Application of the Volume Integral Method of Eddy Current Modeling," J. Nondestructive Eval., 8:45-52 (1989); R. E. Beissner, "Boundary Element Model of Eddy Current Flow Detection in Three Directions," J. Appl. Phys., 60:352-356 (1986). Computer software packages are commercially available for developing models using the VIM and BEM numerical techniques. For example, the "VIC-3D" by Sabbagh Associates, Inc., Bloomington, Indiana is a package for modeling using the VIM, and "FARADAY" by Integrated Engineering Software, Winnipeg, Canada is a package for modeling using the BEM.
Conventional formulations for the VIM and the BEN depend on the coil dimensions and current of the eddy current probe. Typically, solutions or equivalent analytical expressions can be used to determine the magnetic potential field produced by the coil of the eddy current probe. See C. V. Dodd and W. E. Deeds, "Analytical Solutions to Eddy-Current Probe-Coil Problems," J. Appl. Phys., 39:2829-2838 (1968); R. E. Beissner and M. J. Sablik, "Theory of Eddy Currents Induced by a Nonsymmetric Coil Above a Conducting Half-Space," J. Appl. Phys., 56:448-454 (1984); and S. K. Burke, "Impedance of a Horizontal Coil Above a Conducting Half-Space," J. Phys. D: Appl. Phys., 19:1159-1173 (1986). This makes it difficult to model complex eddy current probe geometries and eddy current probe arrays, and impossible to model eddy current probes with ferrite cores or with shielding of any type.